I've been wanting to mix the two for quite some time, but would my efforts be futile? Not just a little of each...I mean a full regiment of each a day. So a regular work out cycle in the morning, then a 3 to 5 mile run in the evening.

Would the cardio after my resistance hurt my body's attempt at healing itself?

Would working out fast twitch and slow twitch muscle fibers on the same day cancel each other out?

I've done it before in the past and I get a lot of weird looks because people think I can't pick a goal and stick with it.

It depends. Resistance training and cardio training can and do compliment each other, and you should be doing both. The application and the purpose are the big questions.

If your goal is to be huge with lots of muscles, then doing excessive cardio will work against that goal. Similarly, if you want to be a marathon runner, lifting excessive weights will give your body little recovery time to heal.

I wouldn't consider running 3-5 miles to be excessive at all, and think you can find balance with that regiment (as long as you realize you will be neither a great runner nor hugely muscular). Though, you would certainly be over training if you did weights and ran more than 4 or 5 days a week (unless you are a triathlete or in already great shape).

when do you plan to rest and let your body heal? i personally feel you should do what you want to when it comes to training. most of the people that are giving you the looks, never go outside the box, as a matter of fact most people who go to the gym just go through the motions thats why they look the same and move the same amount of weight they did last year. just be smart about it, plan it out, maybe set goals. you can also try interval training for your cardio. lets us know whats working for you.